一类Caputo-Fabrizio型分数阶微分方程的三次B样条方法  被引量:2

The Cubic B⁃Spline Method for a Class of Caputo⁃Fabrizio Fractional Differential Equations

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作  者:胡行华[1] 蔡俊迎 HU Xinghua;CAI Junying(School of Sciences,Liaoning Technical University,Fuxin,Liaoning 123000,P.R.China)

机构地区:[1]辽宁工程技术大学理学院,辽宁阜新123000

出  处:《应用数学和力学》2023年第6期744-756,共13页Applied Mathematics and Mechanics

基  金:辽宁省自然科学基金项目(2020-MS-301);教育部人文社会科学研究项目(2021YJCZH204);辽宁省教育厅高等学校基本科研项目(LJ2019JL005;LJ2020ZD002;2022lslwtkt-069)。

摘  要:基于分数阶微积分基本定理和三次B样条理论,构造了求解线性Caputo-Fabrizio型分数阶微分方程数值解的三次B样条方法,利用分数阶微积分基本定理将初值问题转化为关于解函数的表达式,再使用三次B样条函数逼近表达式中积分项的被积函数,进而计算了一类Caputo-Fabrizio型分数阶微分方程的数值解.给出了所构造的三次B样条方法的误差估计、收敛性和稳定性的理论证明.数值实验表明,该文数值方法在求解一类Caputo-Fabrizio型分数阶微分方程数值解时具有一定的可行性和有效性,且计算精度和计算效率优于现有的两种数值方法.Based on the basic theorem of fractional calculus and the cubic B⁃spline theory,the cubic B⁃spline method for numerical solution of linear Caputo⁃Fabrizio fractional differential equations was proposed.The bas⁃ic theorem of fractional calculus was used to transform the initial value problem into an expression about the solution function,and the cubic B⁃spline function was used to approximate the integrand function in the ex⁃pression.Then the numerical solutions of the Caputo⁃Fabrizio fractional differential equations were calculated.The error estimation,convergence and stability of the constructed cubic B⁃spline method were given theoreti⁃cally.Numerical experiments show that,the presented numerical method is feasible and effective in solving a class of Caputo⁃Fabrizio fractional differential equations,and the computation accuracy and efficiency are bet⁃ter than the 2 existing numerical methods.

关 键 词:Caputo-Fabrizio分数阶导数 三次B样条方法 误差估计 收敛性 稳定性 

分 类 号:O241.8[理学—计算数学]

 

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